Answer :
To determine the total momentum of the system after the collision, we'll use the law of conservation of momentum. This principle states that the total momentum of a closed system remains constant if no external forces act on it.
Here's how we solve the problem:
1. Identify the mass and velocity of each hockey player:
- The first player has a mass of 65 kg and is traveling east at a speed of 1.8 m/s.
- The second player has a mass of 70 kg and is traveling west at a speed of 1.4 m/s.
2. Calculate the momentum of each player:
- Momentum is calculated by multiplying mass by velocity.
- For the first player (moving east):
[tex]\[
\text{Momentum}_1 = 65 \, \text{kg} \times 1.8 \, \text{m/s} = 117 \, \text{kg} \cdot \text{m/s}
\][/tex]
- For the second player (moving west, which we'll consider as negative direction):
[tex]\[
\text{Momentum}_2 = 70 \, \text{kg} \times (-1.4) \, \text{m/s} = -98 \, \text{kg} \cdot \text{m/s}
\][/tex]
3. Add the momenta to find the total momentum of the system:
- The total momentum is the sum of the momenta of both players:
[tex]\[
\text{Total Momentum} = 117 \, \text{kg} \cdot \text{m/s} + (-98 \, \text{kg} \cdot \text{m/s}) = 19 \, \text{kg} \cdot \text{m/s}
\][/tex]
Since the resulting total momentum is positive, it indicates the direction of the total momentum is east.
Therefore, the total momentum of the system after the collision is [tex]\(19 \, \text{kg} \cdot \text{m/s}\)[/tex] east. The correct choice is:
A. [tex]\(19 \, \text{kg} \cdot \text{m/s}\)[/tex] east.
Here's how we solve the problem:
1. Identify the mass and velocity of each hockey player:
- The first player has a mass of 65 kg and is traveling east at a speed of 1.8 m/s.
- The second player has a mass of 70 kg and is traveling west at a speed of 1.4 m/s.
2. Calculate the momentum of each player:
- Momentum is calculated by multiplying mass by velocity.
- For the first player (moving east):
[tex]\[
\text{Momentum}_1 = 65 \, \text{kg} \times 1.8 \, \text{m/s} = 117 \, \text{kg} \cdot \text{m/s}
\][/tex]
- For the second player (moving west, which we'll consider as negative direction):
[tex]\[
\text{Momentum}_2 = 70 \, \text{kg} \times (-1.4) \, \text{m/s} = -98 \, \text{kg} \cdot \text{m/s}
\][/tex]
3. Add the momenta to find the total momentum of the system:
- The total momentum is the sum of the momenta of both players:
[tex]\[
\text{Total Momentum} = 117 \, \text{kg} \cdot \text{m/s} + (-98 \, \text{kg} \cdot \text{m/s}) = 19 \, \text{kg} \cdot \text{m/s}
\][/tex]
Since the resulting total momentum is positive, it indicates the direction of the total momentum is east.
Therefore, the total momentum of the system after the collision is [tex]\(19 \, \text{kg} \cdot \text{m/s}\)[/tex] east. The correct choice is:
A. [tex]\(19 \, \text{kg} \cdot \text{m/s}\)[/tex] east.
